Markovian relaxation processes for atoms in vapors and in solids: calculation of free-induction decay in the weak-external-field limit

Abstract

In a previous paper [ J. Opt. Soc. Am. B3, 564 ( 1986)], the validity conditions for the optical Bloch equations were reviewed. It was shown that, even within the limits of an impact or Markovian approximation, the optical Bloch equations fail to account properly for fluctuation-induced changes in atomic transition frequencies. Such changes are properly incorporated in a quantum-mechanical transport equation (QMTE) in which the fluctuation-induced frequency shifts are totally characterized by kernels W(∊′ → ∊) that give the probability density per unit time for a fluctuation to change the frequency shift from ∊′ to ∊. The QMTE describes the interaction of atoms with both an external radiation field and the perturber bath producing the fluctuations. A general method for solving the QMTE as a perturbation series in the external field is presented. Specific calculations are carried out for strong-redistribution, difference [W(∊′ → ∊) is a function of (∊–∊′) only], and Brownian motion kernels. It is shown that, although the kernels possess fundamental differences, they can yield similar results in certain limits. As an example, a perturbation calculation is performed for the free-induction decay (FID) of atoms prepared by a cw laser field and then allowed to radiate when the field is suddenly removed. Radical departures from the predictions of the conventional Bloch equations are found in certain limits, including a first-order contribution to FID in vapors and a nonexponential FID decay for atoms in vapors or solids. The implications of these results to a consistent interpretation of a recent experiment [ Phys. Rev. Lett.50, 1269 ( 1983)] on FID in the impurity ion crystal Pr3+:LaF3 are explored.